Bi-Lipschitz rigidity theorem for dense subgroups of algebraic groups.
problem Characterizing dense subgroups of algebraic groups.
method Bi-Lipschitz rigidity theorem for Zariski dense discrete subgroups.
result No C 1 C^1 C 1 -smooth slim limit set for higher rank semisimple algebraic groups. New theorem about limit points in symmetric spaces.
problem Understanding limit points in symmetric spaces.
method Analyzing Zariski dense discrete subgroups and convex cocompact groups.
result Every limit point of a convex cocompact subgroup is conical.
This paper analyzes the Dawid-Skene model in the dense limit and identifies regions where message passing algorithms fail.
problem Optimality of message passing algorithms in the Dawid-Skene model.
method Analysis of the dense limit of the Dawid-Skene model and identification of regions of sub-optimality.
result Characterization of regions where message passing algorithms do not match Bayes-optimal performance.
In high dimensions, find paths connecting points with intermediate steps in a dense set.
problem Finding efficient paths between points in high-dimensional space using a dense set.
method Constructing step vectors with bounded discrepancy to connect any two points.
result Discrepancy of step vectors is at most 2 2 2\sqrt{2} 2 2 for connecting any two points. Article shows AdS-quasi-Fuchsian groups' limit sets are not smooth.
problem Smoothness of limit sets of AdS quasi-Fuchsian groups.
method Analyzes limit sets of AdS quasi-Fuchsian groups in PO(n,2).
result Limit sets are never C^1, except for Fuchsian groups.
The paper explores graphons of line graphs from sparse finite graphs.
problem Estimating graph limits from sparse finite graphs.
method Mapping finite graphs to their line graphs and analyzing graphs with the square-degree property.
result Graphons of line graphs can distinguish between sparse graphs like star graphs and superlinear preferential attachment graphs.
Busemann points are sparse in Teichmüller spaces.
problem Characterizing the limits of geodesic rays in Teichmüller spaces.
method Proof of nowhere density of Busemann points in horoboundaries.
result Teichmüller metrics lack non-positive curvature.
Proposes dense transformer networks for better pixel-wise predictions.
problem Current deep learning methods for dense prediction are limited by fixed patch sizes.
method Introduces dense transformer networks with learnable patch sizes and shapes.
result Superior performance in natural and biological image segmentation tasks.
Horizon saddle connections imply dense hyperbolic geodesics on dilation surfaces.
problem Characterize dilation surfaces with dense hyperbolic geodesics.
method Analyzing saddle connections and directional flow properties.
result Dilation surfaces with horizon saddle connections have dense hyperbolic geodesics.
Dense neural networks can't approximate all functions.
problem Approximation capabilities of dense neural networks.
method Model compression approach combining weak regularity lemma and graph neural networks.
result Existence of Lipschitz continuous functions not approximable by dense neural networks.
We consider dense 2-generator multiplicative subgroups in C \mathbb C C and show that for each point z ∈ C z\in \mathbb C z ∈ C the set of limit values for the arguments of the powers of each generator at the point z z z is either finite or is [ − π , π ] [-π,π] [ − π , π ]
A dense amalgam connects boundaries of groups split by finite subgroups.
problem Understanding boundaries of groups split by finite subgroups.
method Introducing dense amalgam and applying it to E Z E\mathcal{Z} E Z -boundaries. result Boundaries of groups split by finite subgroups have a dense amalgam structure.
The paper characterizes G G G -ANR spaces and their properties.
problem Characterizing G G G -ANR spaces and their properties for compact groups. method Proving conditions for a metrizable G G G -space to be a G G G -ANR. result Conditions for a metrizable G G G -space to be a G G G -ANR are provided. Generative models can still learn from contaminated data, but with limitations.
problem How much contamination can generative models tolerate?
method Characterized robustness under contaminated enumerations, proving generation is achievable for all countable collections if contamination fraction converges to zero.
result Generation under contamination is achievable for all countable collections if contamination fraction converges to zero, but dense generation is strictly less robust.
In the paper arXiv:1411.4887 [math.AP] it is shown that the set of Riemannian metrics which do not admit global limiting Carleman weights is open and dense, by studying the conformally invariant Weyl and Cotton tensors. In the paper arXiv:1011.2507 [math.DG] it is shown that the set of Riemannian metrics which do not a…
We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a (virtual) simple factor. In particular for rank one or simple Lie groups, Zariski dens…
Study on horospheres in higher rank homogeneous spaces, proving density properties.
problem Density of horospheres in higher rank homogeneous spaces.
method Analyzing maximal horospherical subgroups and their minimal subsets in the context of Furstenberg boundary.
result Equivalence of horospherical limit points and density properties in higher rank homogeneous spaces.
This paper explores loss landscapes of sparse neural networks, finding unique characteristics compared to dense networks.
problem Understanding the loss landscape of sparse neural networks, especially one-hidden-layer networks.
method Analyzes sparse networks with dense and sparse final layers, focusing on linear and non-linear models.
result Sparse networks can have no spurious valleys under certain conditions, but spurious valleys and minima can exist for wide sparse networks.
RDL-Net improves speech enhancement with fewer parameters and better performance.
problem Improving speech enhancement with fewer parameters and better performance.
method Proposes RDL-Net, a CNN combining residual and dense aggregations without over-allocating parameters.
result RDL-Net achieves higher speech enhancement performance with fewer parameters and lower computational requirements.
Sparse sampling method for tensor factorization and completion of high rank tensors.
problem Completion of high rank tensors with missing data in recommendation systems.
method Sparse measurements and message-passing algorithms in a high-dimensional limit.
result Theoretical insights and performance analysis of tensor factorization in dense limit.
Polynomial-time test for detecting dense subgraphs in heterogeneous networks.
problem Detecting a planted community in heterogeneous networks.
method Proposes a polynomial-time test with a standard normal distribution null limiting distribution.
result The test is efficient and performs well in both simulations and real data.
In 1981 Masur proved the existence of a dense geodesic in the moduli space for a Teichmüller space. We prove an analogue theorem for reduced Outer Space endowed with the Lipschitz metric. We also prove two results possibly of independent interest: we show Brun's unordered algorithm weakly converges and from this prove …
Study critical exponents in normal subgroups of higher rank Lie groups.
problem Understanding critical exponents in normal subgroups of higher rank Lie groups.
method Analyzing subgroups and their critical exponents in a higher rank semi-simple Lie group.
result Critical exponents of normal subgroups coincide under certain conditions.
Sparse neural networks can improve performance with less memory.
problem Lack of fast memory limits deep neural network performance.
method Experimented with sparse neural network topologies, including pruning-based and RadiX-Nets.
result Sparse networks achieve comparable accuracy to dense networks but suffer instability at extreme sparsity.
Holomorphic foliations found in ball space with unique properties.
problem Finding holomorphic foliations in the ball space.
method Proving existence of nonsingular holomorphic foliations by closed complex hypersurfaces.
result First example of a holomorphic foliation with complete and incomplete leaves.
The study constructs a dense orbit in the universal commensurability augmented Teichmüller space.
problem Understanding the dense orbit in the universal commensurability augmented Teichmüller space.
method Using isometric embeddings and directed limits of augmented Teichmüller and moduli spaces.
result The action of the universal commensurability modular group on the universal commensurability augmented Teichmüller space produces a dense orbit.
A new algorithm reduces graph complexity for better dense subgraph analysis.
problem Mining dense subgraphs in large graphs for better analysis.
method Multi-stage graph peeling algorithm (M-PA) with two-stage data screening.
result M-PA produces similar dense subgraphs to the previous PA but with reduced graph complexity.
A model of associative memory is studied, which stores and reliably retrieves many more patterns than the number of neurons in the network. We propose a simple duality between this dense associative memory and neural networks commonly used in deep learning. On the associative memory side of this duality, a family of mo…
New tests detect communities in dense bipartite graphs with high accuracy.
problem Detecting communities in dense bipartite graphs with high accuracy.
method Non-asymptotic upper and lower bounds, novel minimax-optimal tests, hard-thresholded nonlinear statistics.
result Non-asymptotic upper and lower bounds match for any configuration of graph sizes.
The Vassiliev conjecture states that the Vassiliev invariants are dense in the space of all numerical link invariants in the sense that any link invariant is a pointwise limit of Vassiliev invariants. In this article, we prove that the Vassiliev conjecture holds in the case of the coefficients of the HOMFLY and the Kau…
Let M M M be a complete metric A N R ANR A N R -space such that for any metric compactum K K K the function space C ( K , M ) C(K,M) C ( K , M ) contains a dense set of Bing (resp., Krasinkiewicz) maps. It is shown that M M M has the following property: If f : X → Y f\colon X\to Y f : X → Y is a perfect surjection between metric spaces, then C ( X , M ) C(X,M) C ( X , M ) with the source limitati…
Research examines coamenable subgroups in higher rank groups.
problem Investigates coamenable normal subgroups in higher rank groups.
method Analyzes three complementary phenomena in higher rank groups.
result Growth indicators of coamenable subgroups are not preserved but the Riemannian critical exponent remains rigid.
Stochastic partition models tailor a product space into a number of rectangular regions such that the data within each region exhibit certain types of homogeneity. Due to constraints of partition strategy, existing models may cause unnecessary dissections in sparse regions when fitting data in dense regions. To allevia…
CRL framework groups features for multivariate learning with sparse and dense problems.
problem Sparse and dense problems in supervised multivariate learning.
method Clustered reduced-rank learning (CRL) with joint matrix regularizations.
result CRL framework is more interpretable and relaxes sparsity assumption.
Study shows essential self-adjointness of wave operators in Lorentzian settings.
problem Essential self-adjointness of wave operators in Lorentzian scattering spaces.
method Using a Fredholm framework to invert the spectral family and refine conclusions.
result Dense range in L^2 for the wave operator acting on an appropriate subdomain.
Extends DAMs to Gaussian distributions for efficient pattern storage and retrieval.
problem Limited storage capacity and retrieval methods for non-vector pattern representations.
method Introduces a log-sum-exp energy function over Gaussian distributions, using optimal transport maps for retrieval dynamics.
result Proves exponential storage capacity and provides quantitative retrieval guarantees.
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…
Introduces new limit spaces for degenerating Calabi-Yau families.
problem Understanding degenerating Calabi-Yau families and their limit structures.
method Introduces galaxy spaces as dense subspace of infinite open Calabi-Yau varieties.
result Galaxy spaces are projective limits of toroidal compactifications.
New method tracks all bees in a hive with high accuracy.
problem Efficient tracking of multiple objects in dense configurations.
method Combining CNNs with U-Net architecture and temporal regularities.
result Near human-level performance with reduced network size.
Study shows properties of Gromov-Hausdorff limit of frame bundles for non-collapsed manifolds.
problem Characterizing the Gromov-Hausdorff limit of orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature.
method Analysis of the Gromov-Hausdorff limit space of orthonormal frame bundles equipped with an almost canonical metric.
result The singular set of the limit space has codimension ≥ 4 \ge 4 ≥ 4 and the complement contains an open and dense C 1 , α C^{1,\alpha} C 1 , α -Riemannian manifold. ARMA nets expand receptive fields for dense prediction tasks.
problem Global information in dense prediction problems is challenging for traditional convolutional layers.
method ARMA layers with adjustable autoregressive coefficients replace traditional convolutions.
result ARMA networks improve dense prediction tasks including video prediction and semantic segmentation.
Effective estimates for lattice orbits in homogeneous spaces.
problem Distribution of lattice orbits in homogeneous spaces.
method Refined techniques on equidistribution of regions under flows.
result Effective convergence of orbit distribution to a limiting density.
Dense Associative Memories outperform classical networks in robustness and signal processing.
problem Improving neural network performance in adversarial attacks and weak signal processing.
method Relaxing replica symmetry in statistical mechanics of spin glasses to analyze unsupervised and supervised learning.
result Explicit analytical investigation of phase diagrams and storage capacities for Dense Associative Memories.
Anosov groups' measures on limit sets are uniquely determined by their dimension.
problem Characterizing measures on limit sets of Anosov groups.
method Higher rank Hopf-Tsuji-Sullivan dichotomy for maximal diagonal actions.
result Uniqueness of Γ Γ Γ -conformal measures for critical dimensions. Generic Hitchin representations generate dense subgroups.
problem Understanding dense subgroups in SL_n(R) representations.
method Using a theorem by Rapinchuk, Benyash-Krivetz, and Chernousov.
result Generic Hitchin representations are strongly dense.
Dense neural networks learn efficiently with large datasets and noise.
problem Training neural networks with large, noisy datasets.
method Statistical mechanics and Monte Carlo simulations.
result Dense neural networks can handle large amounts of patterns and recognize patterns at high signal-to-noise ratios.
New lattices in higher dimensions have dense surface subgroups.
problem Finding dense subgroups in higher-dimensional arithmetic lattices.
method Exhibited nonuniform arithmetic lattices in SO(n,1).
result Contain Zariski-dense surface subgroups.
The paper proves a unique conformal measure for Anosov groups and shows local mixing.
problem Proving the uniqueness of conformal measures for Anosov groups.
method Analogue of Sullivan's theorem for Anosov subgroups of semisimple groups.
result Uniqueness of conformal measures and local mixing for Anosov groups.